Optimal background estimation in EELS

In quantitative electron energy loss spectrometry, it is desirable to estimate the background law below core edge energy in a way that provides the maximum signal-to-noise ratio. Assuming an inverse power background model and independently Poisson distributed measurements, it is shown how to achieve this goal by using a maximum likelihood (ML) estimation technique which provides unbiased and minimum mean square error estimates of all parameters of interest. An efficient and computationally stable implementation of this procedure is proposed. Standard logarithmic least squares estimations are then compared with the ML approach and the gain in performance due to optimal processing is quantified.